• 대한수학회논문집
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• 제35권1호
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• pp.339-345
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• 2020

This note deals with the question of the regularity of (Leray) weak solutions of the Navier-Stokes equations in terms of the pressure. This criterion improves on the existing results.

• International Journal of Aeronautical and Space Sciences
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• 제18권1호
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• pp.1-7
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• 2017

To predict the transonic buffet onset for a supercritical airfoil with shock-boundary layer interactions, a practical steady approach has been proposed. In this study, it is assumed that the airfoil flow is steady even when buffet onset occurs. Steady Navier-Stokes computations are performed on the supercritical airfoil. Using the aerodynamic parameters calculated from Navier-Stokes solver, various steady approaches for predicting buffet onset are discussed. Among the various steady approaches considered in this study, Thomas' criterion based on Navier-Stokes computation has shown to be the most appropriate indicator of identifying the buffet onset for a supercritical airfoil with shock-boundary layer interactions. Good agreements have been obtained compared with the results of unsteady transonic wind tunnel tests. The present method is shown to be reliable and useful for transonic buffet onset for a supercritical airfoil with shock-boundary layer interactions in terms of practical engineering viewpoint.

• 대한수학회지
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• 제45권2호
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• pp.537-558
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• 2008

Consider a weak solution u of the Navier-Stokes equations in the class $L^2((0,T);X_1(\mathbb{R}^d)^d)$. We establish a new approach to treat the regularity problem for the Navier-Stokes equation in term of the multiplier space $X_1(\mathbb{R}^d)$.

• 충청수학회지
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• 제22권3호
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• pp.557-569
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• 2009

We present a new regularity criterion for suitable weak solutions of the steady-state Navier-Stokes equations near boundary in dimension five. We show that suitable weak solutions are regular up to the boundary if the scaled $L^{\frac{5}{2}}$-norm of the solution is small near the boundary. Our result is also valid in the interior.

• 한국광학회지
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• 제4권4호
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• pp.434-441
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• 1993

단일 통과 라만레이저에서 접속 조건에 따른 1차 Stokes 파의 출력특성을 조사하였다. 펌푸빔으로는 Q-switched Nd-YAG 레이저의 기본파인 파장 $1.06{\mu}m$의 빔을 사용하였고 매질로는 고압 메탄을 사용하엿다. 실험 결과 펌프빔을 라만셀로 집속하는 조건에 따라 큰 출력의 치이를 보였는데, 집속상수가 클수록 Stokes 출력이 증가하였다. 이러한 결과는 Stokes와 anti-Stokes의 결합에 의한 이득감소로 이해할 수 있는데, 여기서는 간단한 이론을 통해 집속 조건에 따른 Stokes와 anti-Stokes의 결합의 정도를 알아보고 이득감소 현상을 피하기 위한 집속상수의 기준을 제시하였다. 라만 산란에 수반되는 유도 Brillouin 산란을 측정한 결과 문턱에너지가 집속상수에 비례하여 증가하였고, 이론적으로 이는 다중 모드 레이저를 펌프로 사용할 때 상호작용 거리가 간석성 거리로 제한되어 나타나는 현상으로 이해할 수 있으면 간섭성 거리를 2mm라 했을 때 실험 결과와 비교적 잘 일치하였다.

• Journal of Advanced Research in Ocean Engineering
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• 제2권1호
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• pp.1-11
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• 2016

The objective of this paper is to present an analytical solution in deep water waves and verify the validity of the theory (Shin, 2015). Hence this is a follow-up to Shin (2015). Instead of a variational approach, another approach was considered for a more accurate assessment in this study. The products of two coefficients were not neglected in this study. The two wave profiles from the KFSBC and DFSBC were evaluated at N discrete points on the free-surface, and the combination coefficients were determined for when the two curves pass the discrete points. Thus, the solution satisfies the differential equation (DE), bottom boundary condition (BBC), and the kinematic free surface boundary condition (KFSBC) exactly. The error in the dynamic free surface boundary condition (DFSBC) is less than 0.003%. The wave theory was simplified based on the assumption tanh $D{\approx}1$ in this paper. Unlike the perturbation method, the results are possible for steep waves and can be calculated without iteration. The result is very simple compared to the 5th Stokes' theory. Stokes' breaking-wave criterion has been checked in this study.

• 한국해양공학회지
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• 제36권2호
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• pp.101-107
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• 2022

Dean (1965) proposed the use of the root mean square error (RMSE) in the dynamic free surface boundary condition (DFSBC) and kinematic free-surface boundary condition (KFSBC) as an error evaluation criterion for wave theories. There are well known wave theories with RMSE more than 1%, such as Airy theory, Stokes theory, Dean's stream function theory, Fenton's theory, and trochodial theory for deep-water waves. However, none of them can be applied for deep-water breaking waves. The purpose of this study is to provide a closed-form solution for deep-water waves with RMSE less than 1% even for breaking waves. This study is based on a previous study (Shin, 2016), and all flow fields were simplified for deep-water waves. For a closed-form solution, all Fourier series coefficients and all related parameters are presented with Newton's polynomials, which were determined by curve fitting data (Shin, 2016). For verification, a wave in Miche's limit was calculated, and, the profiles, velocities, and the accelerations were compared with those of 5^th-order Stokes theory. The results give greater velocities and acceleration than 5^th-order Stokes theory, and the wavelength depends on the wave height. The results satisfy the Laplace equation, bottom boundary condition (BBC), and KFSBC, while Stokes theory satisfies only the Laplace equation and BBC. RMSE in DFSBC less than 7.25×10^-2% was obtained. The series order of the proposed method is three, but the series order of 5^th-order Stokes theory is five. Nevertheless, this study provides less RMSE than 5^th-order Stokes theory. As a result, the method is suitable for offshore structural design.

• 한국항공우주학회지
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• 제32권8호
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• pp.37-46
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• 2004

지면효과의 여러 현상을 Navier-Stokes 방정식을 이용하여 해석하고 공기역학적인 관점에서 그 결과를 분석하였다. 2차원 지면효과에 대해서는 이미지 와류에 의한 약형 표면의 압력변화, 두께의 영향, 지면효과의 비점성 유동 현상 등을 확인하였으며, 3차원 지면효과로 익단와류 강도의 증가현상과 유효스팬 증가, 익단와류의 바깥 흐름현상 등을 확인하였다. 또한, 재래식 익형인 NACA 6409와 러시아의 WIG기 전용익형인 DHMTU 8-30에 대해서 Irodov의 조건식을 사용하여 새로 정안정성을 해석하였다. 해석결과, DHMTU 8-30 익형의 세로 정안정성이 NACA 6409 익형보다 훨씬 우수한 것으로 나타났다. 그러므로 DHMTU 8-30을 WIG기에 사용할 경우 NACA 6409에 비해 꼬리날개 부피비를 현저히 줄일 수 있음을 확인하였다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1998년도 추계 학술대회논문집
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• pp.127-132
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• 1998

The present study is aimed to investigate flow characteristics of Two dimensional backward-facing step by numerical approach. A convection conservative difference scheme based upon SOLA algorithm is used for the solution of the two-dimensional incompressible Navier-Stokes equations to simulate the laminar, transitional and turbulent flow conditions at which the experimental data can be available for the backward-facing step. The twenty kinds of Reynolds number are used for the calculations. In an effort to demonstrate that the reported solutions are dependent on the mesh refinement, computations are performed on seven different meshes of uniformly increasing refinement. Also to investigate the result of inflow dependence, two kinds of the inflow profile are chosen for the laminar flow. As criterion of benchmarking the result of numerical simulation, reattachment length is used for the selected Reynolds numbers.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2003년도 가을 학술발표회 논문집
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• pp.235-242
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• 2003

This paper deals with numerical analysis of static and dynamic wind effects on civil engineering structures. Aeroelastic analysis becomes a prime criterion to be confirmed during the structural design because the long-span suspension bridges are prone to the aerodynamic instabilities caused by wind. If the wind velocity exceeds the critical velocity that the bridge can withstand, then the bridge fails due to the phenomenon of flutter. The aeroelastic simulation is carried out using both Computational Fluid Dynamic(CFD) and Computational Structural Dynamic(SCD) schemes.